Systems integrating several sensors are used in a great variety of fields such as site surveillance, maintenance, robotics, medical diagnosis or meteorological forecasting. Such systems for example carry out classification, identification and tracking functions in real time.
To derive the best from multi-sensor systems, it is necessary to use an effective information merging scheme to combine the data originating from the various sensors of the system and generate a decision.
According to the known art, certain information merging schemes rely on Dempster-Shafer theory (theory generalizing probability theory) and thus use belief functions. Belief functions are known for their ability to faithfully represent imperfect information. Information comprising an inaccuracy or an uncertainty or incomplete information is called imperfect information. The sensors of a system are considered to be sources of imperfect information, notably because of their inaccuracy. The term sensor is intended here in the broad sense. It includes physical devices for data acquisition (camera, radar, etc.) but also devices for processing these data. It is possible to establish a belief function on the basis of the data provided by most commercially available sensors. Belief combining schemes can be used. By their very nature these schemes are therefore particularly appropriate to the problem of the merging of imperfect information arising from sensors.
A belief function can be represented with the aid of a function m called the mass distribution defined on a set of proposals Ω which is a space of possible worlds with finite cardinal. It associates degrees of belief, lying between 0 and 1, with parts A (groups of proposals, also called subsets) of Ω. These degrees of belief are determined on the basis of the available information. The set of parts of Ω is denoted 2Ω.                A mass distribution m satisfies the following two conditions:                    the mass ascribed to a subset A lies between 0 and 1: 0≦m(A)≦1, ∀A⊂Ω.            the sum of the masses of all the subsets is equal to one:                        
            ∑              A        ⊆        Ω              ⁢          m      ⁡              (        A        )              =  1
A multi-sensor system of classifier type used for the optical recognition of handwritten characters may be considered by way of nonlimiting example. It is assumed that the system is intended to determine whether the character formed on an image I is one of the letters ‘a’, ‘b’ or ‘c’. We therefore have a set of proposals Ω={a, b, c}. Each of the sensors of the system is a classifier which itself provides an item of information about the character to be recognized in the form of a belief function. It is assumed that there are two sensors of this type in our example. The following table gives an example of a belief function m1 produced by a first sensor of the system and defined on 2Ω.
Am1(A)Ø0{a}0{b}0{a,0.4b}{c}0{a, c}0{b,0.4c}Ω0.2
In this example, the sensor considers that it is as probable that the character to be recognized belongs to {a, b} as that it belongs to {b, c}. (m1({a, b})=m1({b, c})=0.4). m1(Ω)=0.2 represents the ignorance, that is to say the share of doubt, of the sensor.
Dempster-Shafer theory makes it possible to combine the belief functions representing information arising from different sources, so as to obtain a belief function that takes into account the influences of each of the sources. The belief function thus obtained represents the combined knowledge of the various sources of imperfect information (the sensors).
However, systems relying on this theory are based on the assumption that the merged information is independent. In practice two items of information can be considered to be independent if the sources associated with these items of knowledge are wholly unrelated. The concept of independence is fundamental since one of the constraints of information merging is to avoid counting the same item of information twice. It is obvious that this independence assumption is not satisfied by a certain number of multi-sensor systems. For example in the problem of the optical recognition of handwritten characters, the sensors may not be independent. Indeed, according to the known art, shape recognition schemes rely on automatic learning techniques using learning bases. If the sensors have been trained on the same learning bases, that is to say if the sensors have been set up using the same data, then the independence assumption required by the known art merging systems is not satisfied and therefore these systems may not be used.